\chapter{Satellite Radiance Processing}
\label{ch:satellite_radiance}

\section{Overview}
\label{sec:radiance_overview}

Satellite radiance observations represent one of the most significant sources of atmospheric information in modern numerical weather prediction systems. The GSI satellite radiance processing framework implements a sophisticated infrastructure for assimilating measurements from dozens of satellite-borne instruments across the electromagnetic spectrum, from microwave to infrared wavelengths.

The satellite radiance processing system is built around the \texttt{setuprad} framework, which provides a unified interface for handling diverse instrument types while maintaining instrument-specific processing capabilities. This architecture leverages the Community Radiative Transfer Model (CRTM) for forward operator calculations and implements advanced bias correction algorithms to address systematic errors in satellite measurements.

\section{The \texttt{setuprad} Framework}
\label{sec:setuprad_framework}

The \texttt{setuprad} subroutine serves as the master controller for satellite radiance assimilation, orchestrating the processing of observations from multiple instruments through a modular, extensible architecture.

\subsection{Unified Processing Interface}

The \texttt{setuprad} framework implements a standardized interface that abstracts instrument-specific details while providing access to specialized processing capabilities:

\begin{enumerate}
    \item \textbf{Instrument identification and initialization}: Automatic detection of instrument type and loading of appropriate configuration parameters
    \item \textbf{Channel selection and screening}: Application of instrument-specific channel usage decisions and quality control criteria
    \item \textbf{Forward operator invocation}: Integration with CRTM for radiative transfer calculations
    \item \textbf{Bias correction application}: Implementation of multi-variate bias correction algorithms
    \item \textbf{Quality control and screening}: Comprehensive screening procedures adapted to instrument characteristics
\end{enumerate}

\subsection{Instrument-Specific Handlers}

Each instrument type is supported through specialized handler routines that implement instrument-specific processing logic:

\subsubsection{Microwave Temperature Sounders}
\begin{itemize}
    \item \textbf{AMSU-A}: Advanced Microwave Sounding Unit-A processing with cross-track scanning geometry
    \item \textbf{ATMS}: Advanced Technology Microwave Sounder with enhanced spatial resolution
    \item \textbf{MSU}: Microwave Sounding Unit for historical reanalysis applications
\end{itemize}

\subsubsection{Microwave Humidity Sounders}
\begin{itemize}
    \item \textbf{AMSU-B/MHS}: Advanced Microwave Sounding Unit-B and Microwave Humidity Sounder
    \item \textbf{SAPHIR}: Sondeur Atmosphérique du Profil d'Humidité Intertropicale par Radiométrie
    \item \textbf{GMI}: Global precipitation Measurement Microwave Imager
\end{itemize}

\subsubsection{Infrared Hyperspectral Sounders}
\begin{itemize}
    \item \textbf{AIRS}: Atmospheric Infrared Sounder with 2378 spectral channels
    \item \textbf{CrIS}: Cross-track Infrared Sounder with Fourier Transform Spectrometer technology
    \item \textbf{IASI}: Infrared Atmospheric Sounding Interferometer
\end{itemize}

\subsubsection{Geostationary Imagers and Sounders}
\begin{itemize}
    \item \textbf{GOES}: Geostationary Operational Environmental Satellite imager and sounder
    \item \textbf{SEVIRI}: Spinning Enhanced Visible and InfraRed Imager
    \item \textbf{AHI}: Advanced Himawari Imager
\end{itemize}

\section{Configuration System}
\label{sec:radiance_configuration}

The satellite radiance processing system utilizes two primary configuration files that control all aspects of radiance data assimilation: \texttt{radinfo} and \texttt{satinfo}.

\subsection{\texttt{radinfo} Configuration}

The \texttt{radinfo} file provides instrument and channel-specific configuration parameters:

\subsubsection{File Structure}
Each record in \texttt{radinfo} contains:
\begin{verbatim}
instrument  satellite  channel  usage  error  qc_flag  bias_flag  chan_weight
\end{verbatim}

\subsubsection{Channel Usage Control}
Channel usage flags control assimilation behavior:
\begin{itemize}
    \item \textbf{1}: Assimilate channel with full weight
    \item \textbf{0}: Monitor channel without assimilation impact  
    \item \textbf{-1}: Reject channel completely
    \item \textbf{2}: Use for quality control purposes only
\end{itemize}

\subsubsection{Error Specification}
Channel-specific observation error variances account for:
\begin{itemize}
    \item Instrument noise characteristics
    \item Forward model uncertainties
    \item Representativeness errors
    \item Inter-channel error correlations
\end{itemize}

\subsection{\texttt{satinfo} Configuration}

The \texttt{satinfo} file controls bias correction parameters and satellite-specific settings:

\subsubsection{Bias Correction Control}
Configuration parameters for adaptive bias correction:
\begin{itemize}
    \item Predictor selection and weighting
    \item Temporal evolution parameters
    \item Spatial correlation lengths
    \item Convergence criteria and stability constraints
\end{itemize}

\subsubsection{Quality Control Thresholds}
Satellite-specific quality control parameters:
\begin{itemize}
    \item Cloud detection thresholds
    \item Surface type screening criteria
    \item Viewing angle limitations
    \item Brightness temperature range checks
\end{itemize}

\section{Community Radiative Transfer Model Integration}
\label{sec:crtm_integration}

The Community Radiative Transfer Model (CRTM) serves as the forward operator for satellite radiance assimilation, providing the essential capability to simulate satellite observations from atmospheric state variables.

\subsection{CRTM Architecture}

The CRTM implementation in GSI provides:

\subsubsection{Multi-Sensor Support}
Comprehensive instrument database supporting:
\begin{itemize}
    \item Microwave radiometers and sounders
    \item Infrared radiometers and hyperspectral instruments
    \item Visible and near-infrared imagers
    \item Radio occultation instruments
\end{itemize}

\subsubsection{Physical Process Modeling}
Accurate representation of radiative transfer processes:
\begin{itemize}
    \item Gaseous absorption (H₂O, O₃, CO₂, CH₄, N₂O, CO)
    \item Scattering and absorption by clouds and precipitation
    \item Surface emission and reflection properties
    \item Atmospheric temperature and humidity profiles
\end{itemize}

\subsection{Forward Operator Calculations}

The CRTM forward operator computes simulated brightness temperatures:

\subsubsection{Radiance Calculation}
The fundamental radiative transfer equation:
\begin{equation}
I(\nu) = \int_0^{\tau_{surface}} B(\nu, T) \frac{dT}{d\tau} d\tau + \varepsilon(\nu) B(\nu, T_s) e^{-\tau_{surface}}
\end{equation}
where $I(\nu)$ is spectral radiance, $B(\nu, T)$ is the Planck function, and $\tau$ is optical depth.

\subsubsection{Tangent Linear and Adjoint Operators}
Essential for variational data assimilation:
\begin{equation}
\frac{\partial I}{\partial x} = \int_0^{\tau_{surface}} \frac{\partial B}{\partial T} \frac{\partial T}{\partial x} \frac{dT}{d\tau} d\tau + \frac{\partial}{\partial x}\left[\varepsilon B(T_s) e^{-\tau_{surface}}\right]
\end{equation}
where $x$ represents atmospheric state variables.

\subsection{Cloud and Surface Effects}

\subsubsection{Cloud Detection and Handling}
Multi-spectral cloud detection algorithms:
\begin{itemize}
    \item Window channel tests for thick clouds
    \item Split-window techniques for thin cirrus
    \item CO₂ slicing for cloud-top pressure estimation
    \item Dynamic threshold adaptation
\end{itemize}

\subsubsection{Surface Property Modeling}
Accurate surface characterization:
\begin{itemize}
    \item Sea surface emission modeling with wind speed dependence
    \item Land surface emissivity databases with seasonal variations
    \item Snow and ice property parameterizations
    \item Vegetation canopy effects
\end{itemize}

\section{Bias Correction Framework}
\label{sec:bias_correction_framework}

Satellite radiance measurements exhibit systematic biases that must be corrected for optimal assimilation performance. The GSI bias correction system implements sophisticated algorithms for identifying, modeling, and removing these biases.

\subsection{Multi-Variate Bias Correction}

The bias correction model expresses bias as a linear combination of predictor variables:
\begin{equation}
bias(i,k) = \sum_{j=1}^{N_{pred}} \beta_j(i) \cdot P_j(k)
\end{equation}
where $\beta_j(i)$ are channel-dependent bias coefficients and $P_j(k)$ are predictor variables.

\subsubsection{Predictor Variables}
Standard predictors include:
\begin{itemize}
    \item \textbf{Constant term}: Captures systematic instrument offset
    \item \textbf{Thickness variables}: 1000-300 hPa, 200-50 hPa thickness for atmospheric temperature structure
    \item \textbf{Layer-mean temperatures}: Temperature at standard pressure levels
    \item \textbf{Moisture variables}: Column precipitable water, layer humidity
    \item \textbf{Surface variables}: Surface temperature, surface pressure
    \item \textbf{Satellite zenith angle**: Accounts for limb-darkening effects
    \item \textbf{Solar zenith angle**: For solar-affected channels
\end{itemize}

\subsection{Angle-Dependent Bias Correction}

Viewing angle dependencies in satellite measurements require specialized treatment:

\subsubsection{Limb-Darkening Correction}
Zenith angle dependent bias:
\begin{equation}
bias_{angle}(\theta) = \beta_0 + \beta_1 \cos(\theta) + \beta_2 \cos^2(\theta)
\end{equation}
where $\theta$ is the satellite zenith angle.

\subsubsection{Cross-Track Bias Patterns}
Scan-position dependent biases for scanning instruments:
\begin{equation}
bias_{scan}(s) = \sum_{n=1}^{N} a_n \cos\left(\frac{2\pi n s}{S}\right) + b_n \sin\left(\frac{2\pi n s}{S}\right)
\end{equation}
where $s$ is scan position and $S$ is total number of scan positions.

\subsection{Airmass-Based Bias Correction}

Atmospheric airmass effects require specialized correction algorithms:

\subsubsection{Airmass Calculation}
Effective atmospheric path length:
\begin{equation}
AM = \sec(\theta_{sat}) + f(h, \theta_{sat})
\end{equation}
where $f$ accounts for atmospheric refraction and Earth curvature.

\subsubsection{Airmass-Dependent Bias Model}
\begin{equation}
bias_{airmass}(AM) = \gamma_1 \cdot AM + \gamma_2 \cdot AM^2 + \gamma_3 \cdot \ln(AM)
\end{equation}

\section{Advanced Quality Control}
\label{sec:advanced_qc}

Satellite radiance quality control implements sophisticated algorithms that account for instrument characteristics, atmospheric conditions, and surface properties.

\subsection{Multi-Spectral Screening}

\subsubsection{Cloud Detection}
Window channel brightness temperature tests:
\begin{equation}
\Delta T_b = T_{b,window} - T_{b,background} > \Delta T_{threshold}
\end{equation}

Infrared split-window test:
\begin{equation}
T_{11\mu m} - T_{12\mu m} > \epsilon_{cloud}
\end{equation}

\subsubsection{Surface Type Screening}
Specialized screening for different surface types:
\begin{itemize}
    \item Ocean: Sea surface temperature and wind speed consistency
    \item Land: Surface emissivity and temperature relationships  
    \item Snow/Ice: Enhanced scattering and emission characteristics
    \item Mixed pixels: Weighted combination approaches
\end{itemize}

\subsection{Inter-Channel Consistency}

\subsubsection{Spectral Consistency Checks}
For hyperspectral instruments:
\begin{equation}
|\Delta T_b(\nu_i) - \Delta T_b(\nu_j)| < \sigma_{spectral} \cdot \sqrt{|\nu_i - \nu_j|}
\end{equation}

\subsubsection{Cross-Platform Validation}
Simultaneous nadir overpasses (SNO) analysis for inter-satellite calibration monitoring:
\begin{equation}
\Delta T_b^{SNO} = T_{b,sat1} - T_{b,sat2} \pm \sigma_{SNO}
\end{equation}

\section{Channel Selection and Optimization}
\label{sec:channel_selection}

Optimal channel selection maximizes information content while minimizing computational cost and correlated errors.

\subsection{Information Content Analysis}

\subsubsection{Degrees of Freedom for Signal}
Channel information content quantification:
\begin{equation}
DFS = \text{trace}\left[(\mathbf{R} + \mathbf{H}\mathbf{B}\mathbf{H}^T)^{-1}\mathbf{H}\mathbf{B}\mathbf{H}^T\right]
\end{equation}
where $\mathbf{H}$ is the observation operator Jacobian.

\subsubsection{Channel Correlation Analysis}
Inter-channel correlation matrix:
\begin{equation}
\rho_{ij} = \frac{\langle \Delta T_{b,i} \Delta T_{b,j} \rangle}{\sigma_i \sigma_j}
\end{equation}

\subsection{Adaptive Channel Selection}

Dynamic channel selection based on:
\begin{itemize}
    \item Atmospheric conditions (clear, cloudy, precipitating)
    \item Surface type and characteristics
    \item Solar illumination conditions
    \item Data availability and quality
\end{itemize}

\section{Performance Optimization}
\label{sec:radiance_performance}

\subsection{Computational Efficiency}

\subsubsection{CRTM Optimization}
Strategies for efficient radiative transfer calculations:
\begin{itemize}
    \item Profile interpolation and caching
    \item Channel grouping for similar atmospheric sensitivities
    \item Approximate tangent-linear operators for similar channels
    \item Parallel processing across channels and observations
\end{itemize}

\subsubsection{Memory Management}
Efficient handling of large radiance datasets:
\begin{itemize}
    \item Streaming I/O for hyperspectral instruments
    \item Channel subset processing
    \item Observation thinning and super-observation techniques
    \item Memory pooling for CRTM calculations
\end{itemize}

\subsection{Parallel Processing Strategies}

\subsubsection{Domain Decomposition}
Spatial parallelization approaches:
\begin{itemize}
    \item Geographic domain splitting
    \item Orbit-based processing partitions
    \item Load balancing across varying observation densities
\end{itemize}

\subsubsection{Channel Parallelization}
Processing multiple channels simultaneously:
\begin{itemize}
    \item Independent channel processing
    \item Vectorized CRTM calculations
    \item Parallel bias correction computations
\end{itemize}

The satellite radiance processing framework represents one of the most sophisticated components of the GSI system, enabling the effective assimilation of millions of satellite observations through advanced forward modeling, bias correction, and quality control procedures that maximize the information content extracted from these critical observations.